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a(n) = gcd(n, A019565(n)).
4

%I #19 Feb 20 2022 11:00:08

%S 1,1,1,3,1,5,3,1,1,1,1,1,1,1,7,15,1,1,3,1,5,1,11,1,1,1,1,3,7,1,15,1,1,

%T 1,1,1,1,1,1,39,1,1,21,1,1,5,1,1,1,1,1,3,13,1,3,55,7,1,1,1,5,1,1,21,1,

%U 1,3,1,17,1,5,1,1,1,1,3,1,7,3,1,1,1,1,1,1,85,1,3,11,1,3,7,1,1,1,5,1,1,1,3,5,1,51,1,13,7

%N a(n) = gcd(n, A019565(n)).

%H Antti Karttunen, <a href="/A351556/b351556.txt">Table of n, a(n) for n = 0..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = gcd(n, A019565(n)) = gcd(A007947(n), A019565(n)).

%F a(n) = A007947(a(n)).

%F a(n) = A019565(A351558(n)).

%t Table[GCD[n, Times @@ Prime@ Flatten@ Position[Reverse@ IntegerDigits[n, 2], 1]], {n, 0, 105}] (* _Michael De Vlieger_, Feb 20 2022 *)

%o (PARI)

%o A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };

%o A351556(n) = gcd(n, A019565(n));

%Y Cf. A007947, A019565.

%Y Cf. also A324198, A351549, A351557, A351558.

%K nonn,look

%O 0,4

%A _Antti Karttunen_, Feb 19 2022